A process in which propylene is converted into propylene oxide using cumene hydroperoxide obtained from cumene as an oxygen carrier, cumyl alcohol produced together with propylene oxide is subjected to hydrogenolysis to obtain cumene and this cumene is used repeatedly, is disclosed in Czechoslovakia patent CS140743 and JP2001-270880 A. Though these processes are composed of the oxidation step, epoxidation step and hydrogenolysis step, it is difficult to say that they are necessarily sufficient in industrial efficiency.